Question

1. Consider the following spot and forward rates:

1 year spot rate = 4%

3 year spot rate = 5%

4 year forward rate 1 year from now= 6%

Calculate:

1. 2 year forward rate 1 year from now?
2. 2 year forward rate 3 year

Hint: Draw the timeline, plot the given rates to the corresponding intervals and calculate the forward rate for the blank interval.

Answer 1

The principle used here for both problems is the same. There is no arbitrage opportunity and the rates are set accordingly.

a. The three-year spot rate is the rate you will get if you put your money on interest for three years. Hence, it should be the same as putting your money in one year and then again for 2-years after the initial bond expires. Therefore:

(1+0.05)^3 = (1+0.04)x (1+r)^2

r= 5.503%

b. The same concept is used here as well:

(1+0.04) x (1+0.06)^4 = (1+0.05)^3 x (1+r)^2.

Here, we have used the equivalence of putting the money for one year and then for 4 more years; and putting it for three years and then for further 2 years.

r = 6.498%